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Principal component analysis

Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.

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Overview

History

Intuition

Details

Further considerations

Properties and limitations

Computation using the covariance method

Covariance-free computation

Qualitative variables

Applications

Relation with other methods

Generalizations

Similar techniques

Software/source code

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Map overview Semantic statistics

Principal component analysis

Nodes226
Edges225
Triples185
Avg. degree1.99
Density0.00885
Components1

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Principal component analysis

Top relations

related to Software/source code · 59
Principal component analysis → ALGLIB, Analysis, Commercial, Contains PCA, Delphi, EigenDecomp, ELKI, ExPosition, Fortran, Free, FreePascal, GNU Octave, Gretl, Implemented, Implements, In, Integrates PCA, Java, Julia, Kernel PCA
related to Further reading · 24
Principal component analysis → Chapman, Cite, CiteSeerX, Example Using, Exploratory Multivariate Analysis, Hall/CRC The, Husson François, ISBN, Jackson, Jolliffe, Jérôme, London, Lê Sébastien, Multiple Factor Analysis, New York, Pagès Jérôme, Principal Components, Series, Series London, Springer Series
related to history · 21
Principal component analysis → Brooks, Ch, Depending, Eckart, EOF, EVD, Harman, Harold Hotelling, Hotelling, Jolliffe's Principal Component Analysis, Karhunen, Karl Pearson, KLT, Lorenz, Loève, PCA, POD, Sirovich, SVD, XTX
related to External links · 14
Principal component analysis → Andrew Ng, Copenhagen, PCA, Principal Component AnalysisA, Rasmus Bro, Software, Stack OverflowSee, StatQuest, Step-by-Step, University, YouTube, YouTubeA Tutorial, YouTubeLayman's, YouTubeStanford University
see also · 13
Principal component analysis → Canonical, Correspondence, Detrended, Factor, Factorial, Multiple, PCA, PCAL1-norm, PCATransform, Principal, SVD, Wikibooks, Wikiversity
related to Factor analysis · 10
Principal component analysis → Different, Factor, However, If, In, PCA, Principal, Results, The, The PCA
related to Correspondence analysis · 8
Principal component analysis → Because CA, CA, Correspondence, It, Jean-Paul Benzécri, One, PCA, Several
related to Sparse PCA · 5
Principal component analysis → Bayesian, It, PCA, Several, Sparse PCA
related to Independent component analysis · 2
Principal component analysis → ICA, Independent

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Important terminology

pca matrix principal data components analysis displaystyle component variables covariance variance first eigenvectors used also eigenvalues mathbf vector factor value

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
population geneticsinstance ofMany studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points.Principal compon…0.80text
microbiome studiesinstance ofMany studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points.Principal compon…0.80text
and atmospheric scienceinstance ofMany studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points.Principal compon…0.80text
XTX is that the quotient's maximum possible value is the largest eigenvalue of the matrixinstance ofA standard result for a positive semidefinite matrix0.80text
which occurs when w is the corresponding eigenvector.With winstance ofA standard result for a positive semidefinite matrix0.80text
astronomyinstance ofIn fields0.80text
all the signals are non-negativeinstance ofIn fields0.80text
and the mean-removal process will force the mean of some astrophysical exposures to be zeroinstance ofIn fields0.80text
which consequently creates unphysical negative fluxesinstance ofIn fields0.80text
and forward modeling has to be performed to recover the true magnitude of the signalsinstance ofIn fields0.80text
FactoMineRinstance ofthe method is available in the R environment through packages0.80text
spatial intelligenceinstance ofIt was believed that intelligence had various uncorrelated components0.80text

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